On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation

We characterise the subgame perfect equilibrium of a di¤erential market game with hyperbolic inverse demand where …rms are quantity-setters and accumulate capacity over time à la Ramsey. The related Hamilton-JacobiBellman are solved in closed form both on in…nite and on …nite horizon setups and the optimal strategies are determined. Then, we analyse the feasibility of horizontal mergers in both static and dynamic settings, and …nd appropriate conditions for their pro…tability under both circumstances. Static pro…tability of a merger implies dynamic pro…tability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand. JEL Classi…cation: C73, L13